ترغب بنشر مسار تعليمي؟ اضغط هنا

Comultiplication in the Serre Spectral Sequence

177   0   0.0 ( 0 )
 نشر من قبل David Chan
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English
 تأليف David Chan




اسأل ChatGPT حول البحث

We show the homological Serre spectral sequence with coefficients in a field is a spectral sequence of coalgebras. We also identify the comultiplication on the $E^2$ page of the spectral sequence as being induced by the usual comultiplication in homology. At the end, we provide some example computations highlighting the use the co-Leibniz rule.



قيم البحث

اقرأ أيضاً

202 - Thomas Kragh 2015
We construct using relatively basic techniques a spectral sequence for exact Lagrangians in cotangent bundles similar to the one constructed by Fukaya, Seidel, and Smith. That spectral sequence was used to prove that exact relative spin Lagrangians i n simply connected cotangent bundles with vanishing Maslov class are homology equivalent to the base (a similar result was also obtained by Nadler). The ideas in that paper were extended by Abouzaid who proved that vanishing Maslov class alone implies homotopy equivalence. In this paper we present a short proof of the fact that any exact Lagrangian with vanishing Maslov class is homology equivalent to the base and that the induced map on fundamental groups is an isomorphism. When the fundamental group of the base is pro-finite this implies homotopy equivalence.
81 - Guozhen Wang , Zhouli Xu 2017
We show a few nontrivial extensions in the classical Adams spectral sequence. In particular, we compute that the 2-primary part of $pi_{51}$ is $mathbb{Z}/8oplusmathbb{Z}/8oplusmathbb{Z}/2$. This was the last unsolved 2-extension problem left by the recent works of Isaksen and the authors (cite{Isa1}, cite{IX}, cite{WX1}) through the 61-stem. The proof of this result uses the $RP^infty$ technique, which was introduced by the authors in cite{WX1} to prove $pi_{61}=0$. This paper advertises this method through examples that have simpler proofs than in cite{WX1}.
In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3 $-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms $E_m$. In this paper, we introduce $2$-track algebras and tertiary chain complexes, and we show that the $E_4$-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
175 - Weinan Lin 2020
We make a conjecture about all the relations in the $E_2$ page of the May spectral sequence and prove it in a subalgebra which covers a large range of dimensions. We conjecture that the $E_2$ page is nilpotent free and also prove it in this subalgebr a. For further computations we construct maps of spectral sequences which systematically extend one of the techniques used by May and Tangora.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا